The algebra of rewriting for presentations of inverse monoids

We describe a formalism, using groupoids, for the study of rewriting for presentations of inverse monoids, that is based on the Squier complex construction for monoid presentations. We introduce the class of pseudoregular groupoids, an example of which now arises as the fundamental groupoid of our version of the Squier complex. A further key ingredient is the factorisation of the presentation map from a free inverse monoid as the composition of an idempotent pure map and an idempotent separating map. The relation module of a presentation is then defined as the abelianised kernel of this idempotent separating map. We then use the properties of idempotent separating maps to derive a free presentation of the relation module. The construction of its kernel - the module of identities - uses further facts about pseudoregular groupoids.Comment: 22 page

Ultrafast harmonic mode-locking of monolithic compound-cavity laser diodes incorporating photonic-bandgap reflectors

We present the first demonstration of reproducible harmonic mode-locked operation from a novel design of monolithic semiconductor laser comprising a compound cavity formed by a 1-D photonic-bandgap (PBG) mirror. Mode-locking (ML) is achieved at a harmonic of the fundamental round-trip frequency with pulse repetition rates from 131 GHz up to a record high frequency of 2.1 THz. The devices are fabricated from GaAs-Al-GaAs material emitting at a wavelength of 860 nm and incorporate two gain sections with an etched PBG reflector between them, and a saturable absorber section. Autocorrelation studies are reported which allow the device behavior for different ML frequencies, compound cavity ratios, and type and number of intra-cavity reflectors to be analyzed. The highly reflective PBG microstructures are shown to be essential for subharmonic-free ML operation of the high-frequency devices. We have also demonstrated that the single PBG reflector can be replaced by two separate features with lower optical loss. These lasers may find applications in terahertz; imaging, medicine, ultrafast optical links, and atmospheric sensing

Relation modules and identities for presentations of inverse monoids

We investigate the Squier complexes of presentations of groups and inverse monoids using the theory semiregular, regular, and pseudoregular groupoids. Our main interest is the class of regular groupoids, and the new class of pseudoregular groupoids. Our study of group presentations uses monoidal, regular groupoids. These are equivalent to crossed modules, and we recover the free crossed module usually associated to a group presentation, and a free presentation of the relation module with kernel the fundamental group of the Squier complex, the module of identities among the relations. We carry out a similar study of inverse monoid presentations using pseudoregular groupoids. The relation module is defined via an intermediate construction – the derivation module of a homomorphism, – and a key ingredient is the factorisation of the presentation map from a free inverse monoid as the composition of an idempotent pure map and an idempotent separating map. We can then use the properties of idempotent separating maps, and properties of the derivation module as a left adjoint, to derive a free presentation of the relation module. The construction of its kernel – the module of identities – uses further key facts about pseudoregular groupoids

Ordered groupoids and the holomorph of an inverse semigroup

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap operation on an inverse semigroup: for groups these two constructions coincide. We present detailed calculations for semilattices of groups and for the polycyclic monoids.Comment: 16 page

Optically enhanced acoustophoresis

Regenerative medicine has the capability to revolutionise many aspects of medical care, but for it to make the step from small scale autologous treatments to larger scale allogeneic approaches, robust and scalable label free cell sorting technologies are needed as part of a cell therapy bioprocessing pipeline. In this proceedings we describe several strategies for addressing the requirements for high throughput without labeling via: dimensional scaling, rare species targeting and sorting from a stable state. These three approaches are demonstrated through a combination of optical and ultrasonic forces. By combining mostly conservative and non-conservative forces from two different modalities it is possible to reduce the influence of flow velocity on sorting efficiency, hence increasing robustness and scalability. One such approach can be termed "optically enhanced acoustophoresis" which combines the ability of acoustics to handle large volumes of analyte with the high specificity of optical sorting

Role of bulk and surface phonons in the decay of metal surface states

We present a comprehensive theoretical investigation of the electron-phonon contribution to the lifetime broadening of the surface states on Cu(111) and Ag(111), in comparison with high-resolution photoemission results. The calculations, including electron and phonon states of the bulk and the surface, resolve the relative importance of the Rayleigh mode, being dominant for the lifetime at small hole binding energies. Including the electron-electron interaction, the theoretical results are in excellent agreement with the measured binding energy and temperature dependent lifetime broadening.Comment: 4 pages, 3 figure

Pleistocene Brawley and Ocotillo Formations: Evidence for Initial Strike-Slip Deformation Along the San Felipe and San Jacinto Fault Zones, Southern California

We examine the Pleistocene tectonic reorganization of the Pacific–North American plate boundary in the Salton Trough of southern California with an integrated approach that includes basin analysis, magnetostratigraphy, and geologic mapping of upper Pliocene to Pleistocene sedimentary rocks in the San Felipe Hills. These deposits preserve the earliest sedimentary record of movement on the San Felipe and San Jacinto fault zones that replaced and deactivated the late Cenozoic West Salton detachment fault. Sandstone and mudstone of the Brawley Formation accumulated between ∼1.1 and ∼0.6–0.5 Ma in a delta on the margin of an arid Pleistocene lake, which received sediment from alluvial fans of the Ocotillo Formation to the west-southwest. Our analysis indicates that the Ocotillo and Brawley formations prograded abruptly to the east-northeast across a former mud-dominated perennial lake (Borrego Formation) at ∼1.1 Ma in response to initiation of the dextral-oblique San Felipe fault zone. The ∼25-km-long San Felipe anticline initiated at about the same time and produced an intrabasinal basement-cored high within the San Felipe–Borrego basin that is recorded by progressive unconformities on its north and south limbs. A disconformity at the base of the Brawley Formation in the eastern San Felipe Hills probably records initiation and early blind slip at the southeast tip of the Clark strand of the San Jacinto fault zone. Our data are consistent with abrupt and nearly synchronous inception of the San Jacinto and San Felipe fault zones southwest of the southern San Andreas fault in the early Pleistocene during a pronounced southwestward broadening of the San Andreas fault zone. The current contractional geometry of the San Jacinto fault zone developed after ∼0.5–0.6 Ma during a second, less significant change in structural style

Receptor tyrosine kinase inhibitors negatively impact on pro-reparative characteristics of human cardiac progenitor cells

Receptor tyrosine kinase inhibitors improve cancer survival but their cardiotoxicity requires investigation. We investigated these inhibitors' effects on human cardiac progenitor cells in vitro and rat heart in vivo. We applied imatinib, sunitinib or sorafenib to human cardiac progenitor cells, assessing cell viability, proliferation, stemness, differentiation, growth factor production and second messengers. Alongside, sunitinib effects were assessed in vivo. Inhibitors decreased (\u1d631 < 0.05) cell viability, at levels equivalent to 'peak' (24 h; imatinib: 91.5 ± 0.9%; sunitinib: 83.9 ± 1.8%; sorafenib: 75.0 ± 1.6%) and 'trough' (7 days; imatinib: 62.3 ± 6.2%; sunitinib: 86.2 ± 3.5%) clinical plasma levels, compared to control (100% viability). Reduced (\u1d631 < 0.05) cell cycle activity was seen with imatinib (29.3 ± 4.3% cells in S/G2/M-phases; 50.3 ± 5.1% in control). Expression of PECAM-1, Nkx2.5, Wnt2, linked with cell differentiation, were decreased (\u1d631 < 0.05) 2, 2 and 6-fold, respectively. Expression of HGF, p38 and Akt1 in cells was reduced (\u1d631 < 0.05) by sunitinib. Second messenger (p38 and Akt1) blockade affected progenitor cell phenotype, reducing c-kit and growth factor (HGF, EGF) expression. Sunitinib for 9 days (40 mg/kg, i.p.) in adult rats reduced (\u1d631 < 0.05) cardiac ejection fraction (68 ± 2% \u1d637\u1d634. baseline (83 ± 1%) and control (84 ± 4%)) and reduced progenitor cell numbers. Receptor tyrosine kinase inhibitors reduce cardiac progenitor cell survival, proliferation, differentiation and reparative growth factor expression